Computability and Unsolvability (Dover Books on Computer Science)

Book Details

• Author: Martin Davis

• Publisher: Dover

• Edition: New edition

• Binding: Paperback

• Number of Pages: 288

• Release Date: 01-06-1983

• ISBN: 9780486614717

• Package Dimensions: 8.4 x 5.5 x 0.7 inches

• Languages: English

About The Book
In this classic work, Dr. Martin Davis provides a clear and comprehensive introduction to the theory of computability, making it accessible to both specialists and non-specialists at an advanced undergraduate level. The book is divided into three parts, each tackling different aspects of the subject, while maintaining clarity for readers without special mathematical training.

Part One lays the groundwork by introducing the general theory of computability. Topics such as computable functions, operations on these functions, recursive functions, and Turing machines are explored in detail, providing readers with a solid understanding of the fundamental concepts. The author also addresses unsolvable decision problems and the intricacies of self-application, carefully assuming no prior advanced mathematical knowledge in these sections.

In Part Two, Davis shifts focus to applications of the general theory, covering combinatorial problems, Diophantine equations, and mathematical logic. The inclusion of Hilbert's Tenth Problem adds an important dimension to the discussion of unsolvable problems.

Part Three expands on the general theory, diving deeper into the Kleene hierarchy, computable functionals, and the classification of unsolvable decision problems, further developing the concepts introduced earlier.

Originally published in 1958, this pioneering text laid the foundation for much of the terminology used in theoretical computer science today. The new Dover edition includes a preface and an important appendix titled "Hilbert's Tenth Problem Is Unsolvable," which highlights Davis's significant contributions to the field and his ongoing influence. With its clear and stimulating exposition, this book remains a critical resource for anyone interested in the theory of computation.